I do have one DMG that is only on the desktop, and isn't in the Downloads. Has that one been deleted? I can't find it anywhere.

Think of a DMG as a self contained CD in a box. When you double click one, you're "mounting it" and making the OS think you just inserted a CD. Then the folder appears and you access the files that are on the "disk." Then you unmount it and the file folder goes away. You're left with the DMG file to trash/delete or keep to remount another day if necessary.